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has been cited by the following article:

• TITLE: On Cubic Nonsymmetric Cayley Graphs

  AUTHORS: Jingjian Li, Bengong Lou, Rui Wang

  KEYWORDS: Cubic Cayley Graph; Nonsymmetric; Non-Normal

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.3 No.1, January 29, 2013

  ABSTRACT: Let be a connected Cayley graph of group G, then Γ is called normal if the right regular representation of G is a normal subgroup of , the full automorphism group of Γ. For the case where G is a finite nonabelian simple group and Γ is symmetric cubic Cayley graph, Caiheng Li and Shangjin Xu proved that Γ is normal with only two exceptions. Since then, the normality of nonsymmetric cubic Cayley graph of nonabelian simple group aroused strong interest of people. So far such graphs which have been known are all normal. Then people conjecture that all of such graphs are either normal or the Cayley subset consists of involutions. In this paper we give an negative answer by two counterexamples. As far as we know these are the first examples for the non-normal cubic nonsymmetric Cayley graphs of finite nonabelian simple groups.